Encoding the structure of many-body localization with matrix product operators

Pekker, David; Clark, Bryan K.

doi:10.1103/physrevb.95.035116

Encoding the structure of many-body localization with matrix product operators

Journal Article · Mon Jan 09 23:00:00 EST 2017 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.95.035116· OSTI ID:1535826

Pekker, David ^[1]; Clark, Bryan K. ^[2]

Univ. of Pittsburgh, PA (United States); DOE/OSTI
Univ. of Illinois at Urbana-Champaign, IL (United States)

Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. Here, we show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the G_i matrices corresponding to the local ground state on site i and the E_i matrices corresponding to the local excited state. All 2ⁿ eigenstates can be generated from all possible combinations of these sets of matrices.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC); Charles E. Kaufman Foundation; National Science Foundation (NSF)

Grant/Contract Number:: SC0008692; SC0008692

OSTI ID:: 1535826

Alternate ID(s):: OSTI ID: 1338859

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 3 Vol. 95; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Operator entanglement entropy of the time evolution operator in chaotic systems Zhou, Tianci; Luitz, David J. Physical Review B, Vol. 95, Issue 9 https://doi.org/10.1103/physrevb.95.094206	journal	March 2017
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Efficient Representation of Fully Many-Body Localized Systems Using Tensor Networks Wahl, Thorsten B.; Pal, Arijeet; Simon, Steven H. Physical Review X, Vol. 7, Issue 2 https://doi.org/10.1103/physrevx.7.021018	journal	May 2017
Quantum dynamics of thermalizing systems White, Christopher David; Zaletel, Michael; Mong, Roger S. K. arXiv https://doi.org/10.48550/arxiv.1707.01506	text	January 2017
Signatures of the Many-body Localized Regime in Two Dimensions Wahl, Thorsten B.; Pal, Arijeet; Simon, Steven H. arXiv https://doi.org/10.48550/arxiv.1711.02678	text	January 2017

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